{"paper":{"title":"Semidefinite Characterization and Computation of Real Radical Ideals","license":"","headline":"","cross_cats":["math.OC"],"primary_cat":"math.AG","authors_text":"J.B. Lasserre, M. Laurent, P. Rostalski","submitted_at":"2006-09-19T14:32:06Z","abstract_excerpt":"For an ideal $I\\subseteq\\mathbb{R}[x]$ given by a set of generators, a new semidefinite characterization of its real radical $I(V_\\mathbb{R}(I))$ is presented, provided it is zero-dimensional (even if $I$ is not). Moreover we propose an algorithm using numerical linear algebra and semidefinite optimization techniques, to compute all (finitely many) points of the real variety $V_\\mathbb{R}(I)$ as well as a set of generators of the real radical ideal. The latter is obtained in the form of a border or Gr\\\"obner basis. The algorithm is based on moment relaxations and, in contrast to other existing"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0609528","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}